g 105 - 89 r97 _rzewns04ovi5n0ux

Designation: G 105 – 89 (Reapproved 1997) e1

Standard Test Method forConducting Wet Sand/Rubber Wheel Abrasion Tests 1

This standard is issued under the fixed designation G 105; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.

e1 NOTE—Section 12 was added editorially in November 1997.

1. Scope

1.1 This test method covers laboratory procedures for de-termining the resistance of metallic materials to scratchingabrasion by means of the wet sand/rubber wheel test. It is theintent of this procedure to provide data that will reproduciblyrank materials in their resistance to scratching abrasion undera specified set of conditions.

1.2 Abrasion test results are reported as volume loss incubic millimeters. Materials of higher abrasion resistance willhave a lower volume loss.

1.3 Values stated in SI units are to be regarded as thestandard. Inch-pound units are provided for information only.

1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.

2. Referenced Documents

2.1 ASTM Standards:D 2000 Classification System for Rubber Products in Auto-

motive Applications2

D 2240 Test Method for Rubber Property—DurometerHardness3

E 11 Specification for Wire-Cloth Sieves for Testing Pur-poses4

E 122 Practice for Choice of Sample Size to Estimate aMeasure of Quality for a Lot or Process4

E 177 Practice for Use of the Terms Precision and Bias inASTM Test Methods4

G 40 Terminology Relating to Wear and Erosion5

2.2 Other Standard:SAE J200

3. Terminology

3.1 abrasive wear—wear due to hard particles or hard

protuberances forced against and moving along a solid surface(Terminology G 40).

3.1.1 Discussion—This definition covers several differentwear modes or mechanisms that fall under the abrasive wearcategory. These modes may degrade a surface by scratching,cutting, deformation, or gouging(1 and 2).6,7

4. Summary of Test Method

4.1 The wet sand/rubber wheel abrasion test (Fig. 1) in-volves the abrading of a standard test specimen with a slurrycontaining grit of controlled size and composition. The abra-sive is introduced between the test specimen and a rotatingwheel with a neoprene rubber tire or rim of a specifiedhardness. The test specimen is pressed against the rotatingwheel at a specified force by means of a lever arm while thegrit abrades the test surface. The rotation of the wheel is suchthat stirring paddles on both sides agitate the abrasive slurrythrough which it passes to provide grit particles to be carriedacross the contact face in the direction of wheel rotation.

4.2 Three wheels are required with nominal Shore ADurometer hardnesses of 50, 60, and 70, with a hardnesstolerance of62.0. A run-in is conducted with the 50 Durometer1 This test method is under the jurisdiction of ASTM Committee G-2 on Wear

and Erosion and is the direct responsibility of Subcommittee G02.30 on AbrasiveWear.

Current edition approved Aug. 25, 1989. Published October 1989.2 Annual Book of ASTM Standards, Vols 09.02.3 Annual Book of ASTM Standards, Vol 09.01.4 Annual Book of ASTM Standards, Vol 14.02.5 Annual Book of ASTM Standards, Vol 03.02.

6 Available from Society of Automotive Engineers, 400 Commonwealth Dr.,Warrendale, PA 15096.

7 The boldface numbers in parentheses refer to the list of references at the end ofthis standard.

FIG. 1 Schematic Diagram of the Wear Test Apparatus

1

Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.

NOTICE: This standard has either been superseded and replaced by a new version or discontinued.Contact ASTM International (www.astm.org) for the latest information.

wheel, followed by the test with 50, 60, and 70 Durometerwheels in order of increasing hardness. Specimens are weighedbefore and after each run and the loss in mass recorded. Thelogarithms of mass loss are plotted as a function of measuredrubber wheel hardness and a test value is determined from aleast square line as the mass loss at 60.0 Durometer. It isnecessary to convert the mass loss to volume loss, due to widedifferences in density of materials, in order to obtain a rankingof materials. Abrasion is then reported as volume loss in cubicmillimetres.

5. Significance and Use (1-7)

5.1 The severity of abrasive wear in any system will dependupon the abrasive particle size, shape and hardness, themagnitude of the stress imposed by the particle, and thefrequency of contact of the abrasive particle. In this testmethod these conditions are standardized to develop a uniformcondition of wear which has been referred to as scratchingabrasion(1 and 2).Since the test method does not attempt toduplicate all of the process conditions (abrasive size, shape,pressure, impact or corrosive elements), it should not be usedto predict the exact resistance of a given material in a specificenvironment. The value of the test method lies in predicting theranking of materials in a similar relative order of merit aswould occur in an abrasive environment. Volume loss dataobtained from test materials whose lives are unknown in a

specific abrasive environment may, however, be comparedwith test data obtained from a material whose life is known inthe same environment. The comparison will provide a generalindication of the worth of the unknown materials if abrasion isthe predominant factor causing deterioration of the materials.

6. Apparatus 8

6.1 Fig. 2 shows a typical design and Figs. 3 and 4 arephotographs of a test apparatus. (See Ref(4).) Several elementsare of critical importance to ensure uniformity in test resultsamong laboratories. These are the type of rubber used on thewheel, the type of abrasive and its shape, uniformity of the testapparatus, a suitable lever arm system to apply the requiredforce,9 and test material uniformity.

8 Present users of this practice may have constructed their own equipment.Rubber wheel abrasion testing equipment is commercially available. Rubber wheelsor remolded rims on wheel hubs can be obtained through the manufacturer(s).

9 An apparatus design that is commercially available is depicted both schemat-ically and in photographs in Figs. 1-4. Although it has been used by severallaboratories (including those running interlaboratory tests) to obtain wear data, itincorporates what may be considered a design flaw. The location of the pivot pointbetween the lever arm and the specimen holder is not directly in line with the testspecimen surface. Unless the tangent to the wheel at the center point of the area orline of contact between the wheel and specimen also passes through the pivot axisof the loading arm, a variable, undefined, and uncompensated torque about the pivotwill be caused by the frictional drag of the wheel against the specimen. Therefore,the true loading of specimen against the wheel cannot be known.

FIG. 2 Wet Sand/Rubber Wheel Abrasion Test Apparatus

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6.2 Rubber Wheel—Each wheel shall consist of a steel diskwith an outer layer of neoprene rubber molded to its periphery.The rubber is bonded to the rim and cured in a suitable steelmold. Wheels are nominally 178 mm (7 in.) diameter by 13mm (1⁄2 in.) wide (see Fig. 2 and Fig. 5). The rubber willconform to Classification D 2000 (SAE J200).

6.2.1 The 50 Durometer wheel will be in accordance with2BC515K11Z1Z2Z3Z4

where:Z1—Elastomer—Neoprene GW,Z2—Type A Durometer hardness 506 2,Z3—Not less than 50 % rubber hydrocarbon content, andZ4—Medium thermal black reinforcement.


where:Z1, Z3, and Z4 are the same as for 6.2.1, andZ2—Type A Durometer hardness 606 2.


where:Z1, Z3, and Z4 are the same as for 6.2.1, andZ2—Type A Durometer hardness 706 2.

6.2.4 The compounds suggested for the 50, 60, and 70Durometer rubber wheels are as follows:

IngredientContent (pph)

50 60 70

Neoprene GW 100 100 100MagnesiaA 2 2 2Zinc OxideB 10 10 10Octamine 2 2 2Stearic Acid 0.5 0.5 0.5SRF Carbon BlackC 20 37 63ASTM #3 Oil 14 10 10

A Maglite D (Merck)B Kadox 15 (New Jersey Zinc)C ASTM Grade N762

6.2.5 Wheels are molded under pressure. Cure times of 40to 60 min at 153°C (307°F) are used to minimize “heat-to-heat’’ variations.

6.3 Motor Drive—The wheel is driven by a 0.75-kw (1-hp)electric motor and suitable gear box to ensure that full torqueis delivered during the test. The rate of revolution (2456 5rpm) must remain constant under load. Other drives producing245 rpm under load are suitable.

6.4 Wheel Revolution Counter—The machine shall beequipped with a revolution counter that will monitor thenumber of wheel revolutions as specified in the procedure. It isrecommended that the incremental counter have the ability toshut off the machine after a preselected number of wheelrevolutions or increments up to 5000 revolutions is attained.

6.5 Specimen Holder and Lever Arm—The specimen holderis attached to the lever arm to which weights are added so thata force is applied along the horizontal diametral line of thewheel. An appropriate weight must be used to apply a force of222 N (50 lbf) between the test specimen positioned in thespecimen holder and the wheel. The weight has a mass of

FIG. 3 Test Apparatus with Slurry Chamber Cover Removed

FIG. 4 Test Apparatus in Operation

FIG. 5 Rubber Wheel

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approximately 9.5 kg (21 lb) and must be adjusted so that theforce exerted by the rubber wheel on the specimen with therubber wheel at rest has a value of 222.46 3.6 N (50.06 0.8lbf). This force may be determined by calculation of themoments acting around the pivot point for the lever arm or bydirect measurement, for example, by noting the load requiredto pull the specimen holder away from the wheel, or with aproving ring.

6.6 Analytical Balance—The balance used to measure theloss in mass of the test specimen shall have a sensitivity of0.0001 g. A150 g capacity balance is recommended to accom-modate thicker or high density specimens.

7. Reagents and Materials

7.1 Abrasive Slurry—The abrasive slurry used in the testshall consist of a mixture of 0.940 kg of deionized water and1.500 kg of a rounded grain quartz sand as typified by AFS50/70 Test Sand (−50/ +70 mesh, or −230/ +270 µm) furnishedby the qualified source.10

7.2 AFS 50/70 test sand is controlled by the qualified sourceto the following size range using U.S. Sieves (SpecificationE 11).

U.S. Sieve Size Sieve Opening %Retained on Sieve40 425 µm (0.0165 in.) None50 300 µm (0.0117 in.) 5 max70 212 µm (0.0083 in.) 95 min

100 150 µm (0.0059 in.) None Passing

7.2.1 Multiple use of the sand may affect the test compari-sons.

8. Sampling, Test Specimen, and Test Units

8.1 Test Unit—Use any metallic material form for abrasiontesting by this method. This includes wrought metals, castings,forgings, weld overlays, thermal spray deposits, powder met-als, electroplates, cermets, etc.

8.2 Test Specimen—The test specimens are rectangular inshape, 25.46 0.8 mm (1.006 0.03 in.) wide by 57.26 0.8mm (2.256 0.03 in.) long by 6.4 to 15.9 mm (0.25 to 0.625 in.)thick. The test surface should be flat within 0.125 mm (0.005in.) maximum.

8.2.1 For specimens less than 9.5 mm thick (0.375 in.), usea shim in the specimen holder to bring the specimen to a heightof 9.5 mm.

8.3 Wrought and Cast Metal—Specimens may be machinedto size directly from raw material.

8.4 Weld deposits are applied to one flat surface of the testpiece. Double-weld passes are recommended to prevent welddilution by the base metal. Note that welder technique, heatinput of welds, and the flame adjustment of gas welds will havean effect on the abrasion resistance of the weld deposit. Welddeposits should be made on a thick enough substrate, 12.7 mm(0.5 in.) minimum suggested, to prevent distortion. If distortionoccurs, the specimen may be mechanically straightened orground or both.

8.4.1 In order to develop a suitable wear scar, the surface tobe abraded must be ground flat to produce a smooth, level

surface. A test surface without square (90°) edges, having alevel surface at least 50.8 mm (2.00 in.) long and 19.1 mm(0.75 in.) wide, is acceptable if it can be positioned to show thefull length and width of the wear scar developed by the test.

8.5 Coatings—This test may be unsuitable for some coat-ings, depending on their thickness, wear resistance, bond to thesubstrate, and other factors. The criterion for acceptability isthe ability of the coating to resist penetration to its substrateduring conduct of the test. Modified procedures for coatingsmay be developed based on this procedure.

8.6 Finish—Test specimens should be smooth, flat and freeof scale. Surface defects such as porosity and roughness maybias the test results, and such specimens should be avoidedunless the surface itself is under investigation. Exceptingcoatings, the last 0.3 mm (0.01 in.) of stock on the test surface(or surfaces in cases where both major surfaces are to be tested)should be carefully wet ground to a surface finish of about 0.5to 0.75 µm (20 to 30 µin.) arithmetic average as measuredacross the direction of grinding. The direction of the grindingshould be parallel to the longest axis of the specimen. Thefinished surface should be free of artifacts of specimen heattreatment or preparation such as unintentional carburization ordecarburization, heat checks, porosity, slag inclusions, gasvoids, etc.

8.6.1 Thin coatings may be tested in the as-coated conditionsince surface grinding, especially of those less than about 0.3mm (0.01 in.) thick, can penetrate the coating or cause it to beso thin that it will not survive that test without penetration. Thefinish of the substrate test surface prior to coating should besuch to minimize irregularities in the coated surface. Grindingof this surface as directed in 8.6 is suggested for coatings lessthan 0.15 mm (0.005 in.) thick.

8.6.2 The type of surface or surface preparation shall bestated in the data sheet.

9. Procedure

9.1 Thoroughly rinse the slurry chamber before the test toeliminate any remnants of slurry from a previous test.

9.2 Install the rubber wheel of nominal 50 Durometer andmeasure and record its hardness.

9.2.1 Take at least four (preferably eight) hardness readingsat equally spaced locations around the periphery of the rubberwheel using a Shore A Durometer tester in accordance withTest Method D 2240. Take gage readings after a dwell time of5 s. Report average hardness in the form: A/48.6/5, where A isthe type of Durometer, 48.6 the average of the readings, and 5the time in seconds that the pressure foot of the tester is in firmcontact with the rubber rim surface. The 5-s dwell time for thepressure foot in contact with the rubber rim should berigorously adhered to.

9.3 Prior to testing, demagnetize each steel specimen. Thenclean each specimen of all dirt and foreign matter, and degreasein acetone immediately prior to weighing. Materials withsurface porosity (some powder metals or ceramics) must bedried to remove all traces of the cleaning agents that may havebeen entrapped in the material.

9.4 Weigh the specimen to the nearest 0.0001 g.9.5 Set the revolution counter to shut off automatically after

1000 wheel revolutions.10 Available from Ottawa Silica Co., P.O. Box 577, Ottawa, IL 61350.

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9.6 Install the specimen in the specimen holder, using anappropriate shim if the specimen surface is less than 9.5 mmabove the holder seat surface; then install the holder in positionfor testing. Fill the slurry chamber with 1.500 kg of the quartzsand and 0.940 kg of deionized water at room temperature, andplace a cover over the top of the slurry chamber to prevent theslurry from splashing out.

9.7 Start wheel rotation. The rubber wheels are rotated at245 rpm, or 2.28 m/s (449 ft/min) peripheral surface speed.

9.8 Lower the specimen holder carefully against the wheelto prevent bouncing and to apply a force of 222 N (50 lb)against the test specimen. A wear scar is run-in for 1000 wheelrevolutions. Each 1000 revolutions produces 558.6 m (1832.6ft) of lineal abrasion assuming a 177.8 m diameter wheel. Therun-in removes the surface layer and exposes fresh materialthat is not affected by the surface preparation.

9.9 Following the run-in, remove the specimen from theslurry chamber. Clean, dry, and reweigh the specimen to thenearest 0.0001 g. Drain the slurry from the chamber anddiscard it.

9.10 The actual abrasion test is conducted on the same wearscar starting with either the same 50 Durometer rubber wheelused for the run-in, or with another 50 Durometer rubberwheel. It is essential to install the specimen in the specimenholder with the same orientation and position each time.

9.11 Follow the same procedure as used for the run-in,repeating steps 9.1-9.9 with the normally 50, 60, and 70Durometer rubber wheels, in order of increasing hardness.

9.12 Preparation and Care of Rubber Wheels—Dress theperiphery of all new rubber wheels and make concentric to thebore of the steel disk upon which the rubber is mounted. Theconcentricity of the rim shall be within 0.05 mm (0.002 in.)total indicator reading on the diameter. The intent is to producea uniform surface that will run tangent to the test specimenwithout causing vibration or hopping of the lever arm. Thewear scars shall be rectangular in shape and of uniform depthat any section across the width (Fig. 6).

9.12.1 It is recommended that rubber wheels be dressedagain after accumulating approximately 6000 revolutions dur-

ing testing. Experience has shown that more than 6000revolutions may have an adverse effect on the reproducibilityof results.

9.12.2 Dress rubber wheels whenever they develop groovesor striations, or when they wear unevenly so as to developtrapezoidal or uneven wear scars on the test specimen.

9.12.3 The rubber wheel may be used until the diameter isreduced to 165 mm (6.50 in.). The shelf life of the rubber rimmay not exceed two years. Store wheels so that there is noforce on the rubber surface. New rubber rims may be mountedon steel disks by the qualified source.10

9.13 Wheel Dressing Procedure—A recommended dressingprocedure for the periphery of the rubber rim is to mount thewheel on an expandable arbor in a lathe and grind it squarewith a freshly dressed grinding wheel such as a Norton38A60J5VBE, having dimensions of approximately1303 133 13 mm (53 1⁄2 3 1⁄2 in.), rotating at a speed of3500 rpm, while the rubber wheel rotates at 86 rpm. The rubberwheel should be cross-fed at 0.43 mm (0.017 in.) per revolu-tion. After dressing, measure each rubber wheel carefully todetermine the diameter and width of the rubber rim.

10. Calculation of Results

10.1 Test results obtained are three mass loss values ingrams corresponding to the three average Durometer hardnessvalues obtained for the nominally 50, 60, and 70 Durometerrubber wheels. Normalize mass loss values to correspond to thetravel of a wheel having a diameter of 177.8 mm (7.000 in.)and a width of 12.7 mm (0.500 in.) using the followingformula:

Normalized Mass Loss in Grams

5177.83 12.73 Actual Mass Loss~g!

Actual Diameter~mm.! 3 Actual Width~mm.!

or

57.0003 0.5003 Actual Mass Loss~g!

Actual Diameter~in.! 3 Actual Width~in.!

10.2 Plot normalized mass loss values (that is, three valuesfor each sample material) on a logarithmic scale against thecorresponding rubber wheel hardness plotted on a linear scale.The final test result is obtained by fitting a least square line tothe three data points and solving the equation of the line for themass loss corresponding to a rubber hardness of exactly 60Durometer. An example of the procedure is presented inAppendix X1.

10.3 Volume Loss—While 60 Durometer normalized massloss results should be reported and may be used internally intest laboratories to compare materials of equivalent or nearequivalent densities, it is essential that all users of the testprocedure report their results uniformly as volume loss inreports or publications so that there is no confusion caused byvariations in density. Convert mass loss to volume loss asfollows:

Volume Loss, mm3 5Mass Loss~g! 3 1000

Density~g/cm3!

11. Precision and Bias

11.1 The precision and bias of the measurements obtainedwith this test procedure will depend upon strict adherence toFIG. 6 Typical Uniform Wear Scar

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the stated test parameters.11.1.1 The coefficient of correlation (r) for the three mass

loss values determined in a test shall be calculated in accor-dance with Annex A1. The quantityr varies between −1and +1. Either value means that the correlation is perfect;r = 0means that there is no correlation. Data givingr valuesbetween 0.95 and −0.95 should be scrutinized for causes ofscatter.

11.2 The degree of agreement in repeated tests on the samematerial will depend upon material homogeneity, machine andmaterial interaction, and close observation of the test by acompetent machine operator.

11.3 Normal variations in the abrasive material, rubberwheel characteristics, and procedure will tend to reduce theaccuracy of the practice as compared to the accuracy of suchmaterial property tests as hardness or density. Properly con-ducted tests will, however, maintain a 7 % or less coefficient ofvariation of volume loss values that will characterize theabrasion resistance of materials (see Annex A1).

11.4 Initial Machine Operation and Qualification—Thenumber of tests required to establish the precision of themachine for initial machine operation shall be at least five. Thetest samples shall be taken from the same homogeneousmaterial.

11.4.1 The standard deviation from the mean average shallbe calculated from the accumulated test results and reduced tothe coefficient of variation in accordance with Annex A1. Thecoefficient of variation shall not exceed 7 % in materials of the

2 to 60 mm3 volume loss range. If this value is exceeded, themachine operation shall be considered out of control and stepstaken to eliminate erratic results.

11.4.2 In any test series all data must be considered in thecalculation, including outliers (data exceeding the obviousrange). For example, an exceedingly high or low volume lossmust not be disregarded except in the case of observed faultymachine operation, or obvious test specimen anomaly.

11.5 While two or more laboratories may develop test datathat is within the acceptable coefficient of variation for theirown individual test apparatus, their actual averages may berelatively far apart. The selection of sample size and themethod for establishing the significance of the difference inaverages shall be agreed upon between laboratories and shallbe based on established statistical methods Practice E 122,Practice E 177, andASTM STP 15D.11

11.6 Reference materials should be used for periodic moni-toring of the test apparatus and procedures in individuallaboratories. (A satisfactory reference material for this test hasnot yet been established through laboratory testing.)

12. Keywords

12.1 abrasive wear test; metallic materials; rubber wheel;scratching abrasion; wet sand

ANNEX

(Mandatory Information)

A1. SOME STATISTICAL CONSIDERATIONS IN ABRASION TESTING

A1.1 Background—The wet sand/rubber wheel abrasiontest as developed and described by Haworth, Borik, and others(see Refs(1-4), p. 18) has been in various stages of evolutionand use over the last two or more decades. A number ofvariations of this test procedure have been used by severalresearch and industrial laboratories in the United States whowere faced with the problem of evaluating hardfacing alloys,castings, and wrought products for their resistance to abrasivewear. Individual laboratories set their own test parameters withthe goal being the generation of reproducible test data withinthe laboratory. As the need for standardization became appar-ent, in 1962 The Society of Automotive Engineers establisheda division (No. 18) of the Iron and Steel Technical Committee(ISTC) to achieve this end. This was not accomplished and in1983, subcommittee G02.30 formed a task group with theobjective of producing an ASTM Standard Practice. In previ-ous round-robins conducted by the SAE group, it has beenevident that the variability of experimental error inherent ineach laboratory is a factor that must be considered. Not onlymust the test method, apparatus, and individual operatorgenerate correct results (bias) but the test results must beconsistently reproducible (precision) within an acceptable

narrow range. Another important consideration in developingaccurate and precise test results is the selection of adequatesample size. More specifically this was the need for laborato-ries to agree on the number of times a test should be repeatedon a given homogeneous material in order to obtain a mean-ingful average result. While the single test results and simplearithmetic averaging may in some few cases be useful inindividual laboratories, it is essential that statistical techniquesand multiple testing of specimens be utilized for the qualifica-tion of each test apparatus, and for the comparison of materials.Further information on statistical methods may be found inPractice E 122,STP 150, and in the references.

A1.2 Statistical Formulas—Several formulas for the cal-culation of optimum sample size, standard deviation, andcoefficient of variation are used in the statistical analysis ofdata. To ensure uniformity among laboratories using the wetsand/rubber wheel test, the standard deviation and coefficientof variation of results produced from a series of tests shall becalculated by the following formulas:s = standard deviation (small sample size, 2 to 10) = R/d2 (1)s = standard deviation (any sample size) (2)

11 Manual on Presentation of Data and Control Chart Analysis, ASTM STP 150,ASTM, 1976.

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= =(~x 2 x!2/~n 2 1!V = % coefficient of variation = (s/x) 3 100 (3)n = sample size (95 % confidence level)

= (1.96 V/e)2 (4)

where:s = standard deviation from the mean,V = variability of the test procedure, %,x = value of each test result (volume loss in mm3),x = mean of arithmetic average for n tests,(x = sum total of all test values,n = number of tests or observations,e = allowable sampling error, %,R = difference between the highest and lowest test value,

andd2 = deviation factor, which varies with sample size

(Table A1.1)

A1.3 Use of Statistical Methods—In evaluating the preci-sion and accuracy of any test procedure, new users must dealwith the concepts of mean averages, standard deviation fromthe mean, variability of test results, range of results, allowablesampling error, and particularly the effect of sample size. Whileit is obvious that a large number of tests on the same materialis desirable and will yield a high confidence level in evaluatingtest results, many abrasion test evaluations are made on a smallnumber of samples. This is due to the fact that in muchabrasion work, large numbers of test specimens are just notavailable. In addition to this a new user is concerned withevaluating the accuracy of his first few (2 or 3) test resultsduring the initial test campaign which certainly should notinspire much confidence because of the small number of tests.However, even with this admittedly small sample size, the usermay calculate the variability of results, which may give ageneral indication of precision of the apparatus and testmethod. As more data are accumulated from the same homo-geneous material and new data are accumulated from differentmaterials, the accumulated variability values may be averagedto provide a better estimate of the precision of the apparatusand procedure.

A1.4 Small Sample Size (2 to 10):

A1.4.1 In statistical analysis the estimated standard devia-tions of large sample sizes (over 10) are derived from thesquare root of the mean square of deviations from the average.

A typical user of this test procedure will more likely start outwith less than 10 test results. In these cases the standarddeviation(s) is more efficiently derived from the range (R) ofthe sample observation than from the root mean square. Forsuch samples the standard deviation is obtained by multiplyingthe range of available observations (the difference between thehighest and lowest numerical value) by a deviation factor(Formula 1) that varies with the sample size. Once the standarddeviation is obtained, the percent coefficient of variation isattained by dividing the standard deviation by the average testvalue x and multiplying by 100. The deviation factor isobtained from Table A1.2.

A1.4.2 Example 1—This example shows typical analysisfor standard deviation and coefficient of variation of actual datafrom three abrasion tests made upon a Co-Cr-C hardfacingalloy deposit.Number of tests (n) = 3,Volume loss data (x) = 13.7 mm3, 15.5 mm3, 17.9 mm3,Average of volume loss (x) = 15.7 mm3,Range of test = 4.2 mm3,Standard deviation (s) = 4.2

1.693 5 2.36,Coefficient of variation (v) = (s/x) 3 100 = (2.36/15.7) 3 100 = 15.0 %.

A1.4.2.1 Note that the 15.0 % variation is well above theacceptable 7 % maximum as indicated in 11.4.1 of the stan-dard. It is obvious that either this particular test apparatus orprocedure was out of control, or the variability of the hardfac-ing deposit was such to cause this large variation in test results.

A1.5 Large Sample Size (10 or Over):

A1.5.1 Example 2—This example shows the analysis forthe coefficient of variation of ten abrasion tests made uponnormalized 1090 steel. The standard deviation was calculatedfrom Formula 2 and the test data are set down in the followingformat:

Test Number x x − x (x − x)2

1 6.02 −0.43 0.18492 6.34 −0.31 0.09613 6.75 0.10 0.01004 5.64 1.01 1.02015 6.52 −0.13 0.01696 7.08 .43 0.18497 6.26 −0.39 0.15218 6.96 0.31 0.09619 6.85 0.20 0.0400

10 6.07 −0.58 0.3364

x = 6.45 2.1375 = ((x − x)2

s = =(~x 2 x!2/~n 2 1! = =2.1375/9 = =0.2375 = 0.4873V = (s/x) 3 100 = (0.4873/6.45) 100 = 7.56 %

A1.5.1.1 In this particular test series the 7.56 % coefficientTABLE A1.1 Minimum Acceptable Sample Size ( n) for 95 %Confidence Level

Allowable Sampling Error ( %)

Coefficient of Variation (V)

n 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 10 %

1 4 1 ... ... ... ... ... ... ...2 16 4 2 1 ... ... ... ... ...3 35 9 4 3 2 1 ... ... ...4 62 16 7 4 3 2 2 ... ...5 96 24 11 6 4 3 2 2 16 ... 35 16 9 6 4 3 2 27 ... 47 21 12 8 6 4 3 28 ... 62 28 16 10 7 5 4 39 ... 78 35 20 13 9 7 5 4

10 ... 96 43 24 16 11 8 6 4

TABLE A1.2 Factors for Estimating Standard Deviation from theRange on the Basis of Sampling Size

Sample Size (n) d2 1/d2

2 1.128 0.88653 1.693 0.59074 2.059 0.48575 2.326 0.42996 2.534 0.39467 2.704 0.36988 2.847 0.35129 2.970 0.3367

10 3.078 0.3249

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of variation indicated the test procedure was slightly outside ofsatisfactory control.

A1.6 Estimated Sample Size and Allowable SamplingError:

A1.6.1 As indicated previously the availability of multipletest specimens in abrasion testing is sometimes limited. Whenthis occurs the user must have some criterion upon which tojudge the minimum acceptable sample size for meaningfulresults. Practice E 122 describes the choice of sample size toestimate the average quality of a lot or process. The followingformula takes into account the allowable sampling error andthe inherent variability of experimental error of the test method(coefficient of variation),

n 5 ~1.96v/e!2

A1.6.2 Table A1.1 is based upon this formula. It indicates a5 % probability that the difference between the sample estimateof the mean valuex, and that obtainable from averaging allvalues from a very high number of tests, will exceed theallowable sampling error (e). This corresponds to a 95 %confidence level which is an appropriate criterion for abrasiontests. For example, if the coefficient of variation of the testapparatus as determined by multiple testing is 7 %, theminimum sample size (n) would be 8 in order to obtain a 5 %allowable sampling error. Note, however, that if the test resultsfor the 8 samples does not generate a coefficient of variation of7 % or less, the test is not valid and corrective action must betaken.

A1.7 Typical Volume Loss Values—The wet sand/rubberwheel test will produce volume losses in metallic materialsranging from about 0.25 to 100 mm3. The more abrasion-resistant materials will develop the least volume loss. TableA1.3 shows typical volume loss ranges that may be expected inthe metals listed. These test data were obtained in the last SAEround-robin and represent a population between differentlaboratories. Within the same laboratory, reproducibility of testresults will be better than the values shown. They are offered asguidelines only and not as purchasing specifications or asstandard reference specimens. Any material specificationsinvolving this test method must be by agreement between theseller and the purchaser. When volume losses are less than 1mm3, greater accuracy in material ranking may require amodified procedure, for example, use of 5000 revolutions perrubber wheel.

APPENDIX

(Nonmandatory Information)

X1. SAMPLE COMPUTATION OF MASS LOSS AT 60 DUROMETER HARDNESS BY MEANS OF A LEAST SQUARE LINE

X1.1 Given the following:X (Durometer

Hardness)X1 = 50.1 X2 = 59.0 X3 = 66.0

W (WeightLoss, g)

W1 = 0.201 W2 = 0.523 W3 = 1.006

Y (Logarithmof WeightLoss)

Y1 = −0.69680 Y2 = −0.28150 Y3 = 0.00260

X1.1.1 Least Square Line Equation:

Y5 Y1(XY2

(X(YN

(X2 2~(X! 2

N

~X 2 X! (X1.1)

where:Y = logarithm of weight loss = LogW,X = durometer hardness,Y = average ofY,X = average ofX,N = 3 (number of points), and( = Sum

X1.1.1.1 Determination of Individual Terms in (Eq X1.1):

Y = 20.696802 0.281501 0.002603 5 2

0.32523,(XY = (50.1)(−0.69680) + (59.0)(−0.28150) +

(66.0)(0.00260) = 51.34679,(X(Y = (50.1 + 59.0 + 66.0)(−0.69680 − 0.28150 + 0.00260)

= 170.84577,(X2 = (50.1)2 + (59.0)2 + (66.0)2 = 10347.01,((X)2 = (50.1 + 59.0 + 66.0)2 = 30660.01, andX = 50.11 59.01 66.0

3 5 58.36667.

X1.1.1.2 By Substitution Into (Eq X1.1):

Y5 20.325231251.346792

2170.845773

10347.01230660.01

3

~X 2 58.36667!

(X1.2)

TABLE A1.3 Typical Volume Loss Range

MaterialVolume Loss,

mm3SpecificGravity

1. 304 Stainless Steel bar HRB 78 55 6 14 8.02. T-1 Low Alloy Steel bar HRC 24 20 6 7 7.863. AISI 1090 Steel plate normalized 900°C

HRC 306.7 6 2.0 7.84

4. AISI D2 Tool Steel hardened and temperedHRC 60

1.2 6 0.2 7.6

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or

Y5 20.325231 0.04411~X 2 58.36667!

At X = 60, the logarithm of the normalized weight loss canbe computed from (Eq X1.2):

Y5 20.325231 0.04411~602 58.36667! (X1.3)

Y5 20.253195 Log W

W5 0.558 grams

X1.1.2 Coeffıcient of Correlation:X1.1.2.1 The coefficient of correlation,r, a measure of

scatter around the least equal line is computed according to thefollowing expression:

r 5 6Œ(~Yest2 Y!2

(~Y2 Y!2 (X1.4)

where:((Yest− Y)2 = (Y1est− Y)2 + (Y2est− Y)2 + (Y3est− Y)2,and((Y − Y)2 = (Y1 − Y)2 + (Y2 − Y)2 + (Y3 − Y)2

X1.1.2.2 Using Equation of the Least Square Line (EqX1.2) and substituting values ofX1, X2 andX3, as given, theY1est, Y2est andY3est are calculated as follows:

Y1est5 20.325231 0.04411~X1 2 58.36667!

For X1 = 50.1,Y1est= −0.68987

Y2est5 20.325231 0.04411~X2 2 58.36667!

For X2 = 59.0,Y2est= −0.29729

Y3est5 20.325231 0.04411~X3 2 58.36667!

For X3 = 66.0,Y3est= 0.01148

REFERENCES

(1) Avery, H. S., “The Nature of Abrasive Wear,”SAE Preprint 750822,Society of Automotive Engineers, 1975.

(2) Avery, H. S., “Classification and Precision of Abrasion Tests,”SourceBook on Wear Control Technology, ASM, 1978.

(3) Haworth, R. W., Jr.,“ The Abrasion Resistance of Metals,”Transac-tions ASM, Vol 41, 1949, pp. 819–854.

(4) Borik, Frank,“ Rubber Wheel Abrasion Test,”SAE Paper 700687,Society of Automotive Engineers, 1970.

(5) Stolk, D. A., “Field and Laboratory Tests on Plowshares,”SAE Paper

700690, Society of Automotive Engineers, 1970.(6) Saltzman, G. A., “Wet Sand Rubber-Wheel Abrasion Test for Thin

Coatings,”Selection and Use of Wear Test for Coatings, ASTM STP769, R. G. Bayer, Ed., ASTM, 1982, pp. 71–91.

(7) Saltzman, G. A., Merediz, T. O., Subramanyam, D. K., and Avery, H.S., “Experience with the Wet Sand/Rubber Wheel Abrasion Test,”Slurry Erosion: Uses, Applications, and Test Methods, ASTM STP 946,J. E. Miller and F. E. Schmidt, Jr, Eds., ASTM 1987, pp. 211–242.

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